Heat olive oil in a large soup pot or Dutch oven over medium heat.

Add the finely chopped carrots, celery, and shallots or onions. Season with salt and pepper, and cook for 8 to 10 minutes until softened.

Add minced garlic, poultry seasoning, and dried thyme. Sauté for 1 to 2 minutes until fragrant.

Pour in chicken stock or broth and increase heat to high. Cover and bring to a boil.

Once boiling, add halved chicken breasts, cover again, and reduce heat to low. Simmer for 10 to 12 minutes until fully cooked.

Remove chicken and shred or chop it after cooling. Refrigerate until needed.

Stir in wild rice to the pot with the broth and vegetables. Cover and simmer for 20 to 30 minutes until al dente.

Melt butter in a separate saucepan over medium heat. Whisk in gluten-free flour for 1 minute.

Gradually pour in milk while whisking to make a creamy sauce. Cook 1 to 2 minutes until thickened, then remove from heat.

Whisk the creamy mixture into the pot with broth and rice. Add shredded chicken and let simmer for 5 minutes until thickened.

Taste and adjust seasoning as necessary. Allow soup to rest for 5 to 10 minutes before serving.